Multiply and simplify the following complex numbers: $({1-5i}) \cdot ({3-2i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1-5i}) \cdot ({3-2i}) = $ $ ({1} \cdot {3}) + ({1} \cdot {-2i}) + ({-5i} \cdot {3}) + ({-5i} \cdot {-2i}) $ Then simplify the terms: $ (3) + (-2i) + (-15i) + (10i^2) $ Imaginary unit multiples can be grouped together. $ 3 + (-2 - 15)i + 10 i^2 $ After we plug in $i^2 = -1$, the result becomes $ 3 + (-2 - 15)i - 10 $ The result is simplified: $ (3 - 10) + (-17i) = -7-17i $